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Current time:0:00Total duration:9:09

welcome back I'm not going to do a bunch of projectile motion problems this cuz I think you'll learn more just seeing someone do it and thinking out loud maybe than all the formulas and I have a strange notion that I might have done more harm than good by confusing you with a lot of what I did in the last couple of videos so hopefully I can I could undo any damage if I have done any or even better hopefully you did learn from those and we'll just add to the learning so let's start with both start with a problem let's just art with a general problem let's say I'm at the top of a cliff and I jump so instead of throwing something I just you know I just jump off the cliff and you know what we won't worry about my my motion from side to side we just assume I go straight down we could you know you can even think that someone just dropped me off of the top of a cliff I know these these are getting kind of morbid lit but let's just assume that nothing bad happens to me so let's say that at the top of the cliff my velocity so my initial velocity velocity initial is going to be zero right because I'm I'm stationary before the person drops me or before I jump right and let's say at the bottom of the cliff my velocity is let's say it is 100 meters per second so my question is what is the height of this cliff so what is and actually you know what let me let me I think this is a good time to actually introduce the the direction notions of velocity that show you this scalar quantity so let's just assume up is positive and down is negative so my velocity is actually 100 meters per second down I could have assumed the opposite so velocity the final velocity is a hundred meters per second down and since we are saying that down is negative and gravity is always pulling you down we're going to say that our acceleration is equal to gravity which is equal to minus ten meters per second squared and this is you know gravity I destroyed that by ahead of times because when we're dealing with anything of throwing or jumping or anything on this planet we could just use this constant and the actual number is like 9.81 but I want to be able to do this without a calculator so I'll just I'll just stick with minus 10 meters per second squared so it's pulling me down that's why the minus is there so my question is okay I know my initial velocity I know my final velocity right before I hit the ground all right when I hit the ground what's the distance and in this circumstance what does distance represent distance it would be the height of the cliff so how do we figure this out huh well what's the only formula that we know for distance well we know that actually it's really the change in distance but in this case it's the same thing so change in distance is equal to the average velocity and you know when you learned this in middle school or wherever probably even elementary school you didn't say average loss because you always assume velocity was constant so the average and the instantaneous velocity was kind of the same thing but now since the velocity is changing we're going to say the average velocity so just the change in distance is equal to the average velocity times time and this should be intuitive to you this at this point I mean velocity really is just distance divided by time or actually change in distance divided by times change in time change in distance divided by change in time is velocity so actually let me change this to change in time right but since we always assume or we normally assume that we start a distance is equal to zero and we assume that we assume we start at time is equal to 0 we can write distance is equal to velocity average times time maybe later on we'll do situations where we're not starting at time 0 or distance 0 and in that case we will have to build more formal and say it's change in distance is equal to velocity average velocity times average times the change in time sorry I'm messing up all the terminology anyway this is the formula we know and so let's see what we can figure out can we figure out the average velocity well the average velocity is just the average of the initial velocity and the final velocity so the average velocity is just equal to the average of these two numbers so minus 100 plus zero over two I'm just averaging the numbers equals minus 50 meters per second so we were able to figure that out what can we figure out time well we know also that velocity or let's say the change in velocity so change in velocity change in velocity is equal to the final velocity minus the initial velocity right nothing nothing fancier this is you don't have to memorize this this hopefully is intuitive to you that the change is just the final velocity minus initial velocity and then that equals acceleration times time right so what's the change in velocity in this situation well the final velocity is minus 100 meters per second and then the initial velocity is zero so that equals the change in velocity is equal to minus 100 meters per second I'm kind of jumping in and out of the unit's but I think you get what I'm doing and that equals acceleration times time well what's the acceleration it's minus ten meters per second squared because I'm going straight down minus ten meters per second squared times time this is pretty straightforward equation right divide both sides by the acceleration by the minus ten meters per second squared and you will get time is equal to the negatives cancel out and as they should because well write the negative time is a difficult well we're assuming positive time and then it's good we got a positive time answer but the negatives cancel out and we get time is equal to ten seconds so there we have it we've figured out time we figured out the average velocity so now we could figure out the height of the cliff the distance is equal to the average velocity minus 50 meters per second times 10 seconds so the distance this is going to be an interesting notion to you the disk is going to be - 500 - 500 meters so this might not make a lot of sense to you what is what is - 500 meters mean well this is actually right because it's actually this formula is actually the change in distance change in distance right we said if we did formally it would be their change in distance so if we have a cliff let me change colors so that it looks like a cliff so if we have a cliff and if we assume that we start that this that this point right here is distance is equal to zero then the ground the ground if this if this cliff is 500 meters high your final distance so this is the initial distance your final distance DF is actually going to be at minus 500 meters right we could have done it the other way around where we could said this is plus 500 meters and then this is zero but all that matters is really the change in distance right we're saying from the top of the cliff to the ground the change in distance is minus 500 meters and - based on our convention we said - is down so the change is 500 meters down and that's the height of the cliff so that's pretty interesting if you go to a 500 meter cliff so that's that's what that's roughly the size of a let's see 500 meters is about 1,500 feet so that's that's roughly the size of you know that may be a very tall skyscraper like the World Trade Center or the Sears Tower so if you jump off of something like that this will be no air resistance which is a big assumption or let's say if you were to drop a penny because a penny has very little air resistance if you were to drop a penny off of the top of a Sears Tower or some building like that at the bottom it will be going 100 meters per second so extremely fast and that's why you shouldn't be doing it because that is fast enough to kill somebody and I don't want to give you any bad ideas if you're a bad person but it's just interesting that physics allows you to solve these types of problems so in the next presentation I'm just going to keep doing problems and and hopefully you'll realize that everything really just boils down to average velocity but change in velocity is acceleration times time and change in distance is equal to change in is equal to change in time times average velocity which we all did or just now so I'll see in the next presentation